We offer a hybrid (trinomial tree plus semi-analytic formulas) pricing method for the product. Currently, the model uses spot implied volatility for the first time window, and forward implied volatility for the second time window. These are Black-Scholes implied volatilities from traded vanilla European options, but, while desired, usage of different volatilities based on strike or barrier moneyness directly within the tree is difficult to achieve.
This product can be seen as a special case of a complex barrier option, where we can have multiple single and double partial barrier (partial barrier meaning: the barrier is effective only on a subinterval of the full option term).
Currently, the model uses spot implied volatility for the first time window, and forward implied volatility for the second time window. These are Black-Scholes implied volatilities from traded vanilla European options, but, while desired, usage of different volatilities based on strike or barrier moneyness directly within the tree is difficult to achieve.
We will start by defining Single Knock Out Partial Barrier Option, Single Knock In Barrier Option, Double Knock Out Partial Barrier Option, and Double Knock In Barrier Option contracts on whose features the Double Window Double Barrier Option contract definition is based. The exercise style is assumed European everywhere.
The Single Knock In Barrier (SKIB) Option has one knock in barrier effective for the whole term of the option (we do not define here a general partial version for knock in). Let B be the single barrier. The possible types of Single Knock In Barrier Option contract are: up-in-call/put (UIC/P), down-in-call/put (DIC/P).
References: